You might also be interested in the detail table (B02001) that has just population and MOE estimates. I've generated a link using 5-year ACS data for population by county, here: factfinder.census.gov/.../0100000US.05000.003
You could also search "B02*" or "C02*" to get similar results for specific race groups. I link to 5-year data because 1-year data is only available for counties with a population of 65,000 or more. You'll have to use 5-year data if you want every county.

And this is a great place to start when you want a subject table: www.census.gov/.../
(Tip: Click Show All in the top left corner to see all the subjects at once.)

It might also be useful for you research to know that Census' Intercensal Population Estimates are available at the county level by race/ethnicity. Those can be found here: www.census.gov/.../counties-detail.html
Notably, the overall total will match up with ACS data, because ACS's county population totals are forced to match the Intercensal Population Estimates. The ACS tables indicate this by using "****" in the MOE column. This controlling does not happen for population totals by race at the county level though.